Heavy-ion Fusion-fission Reactions Research Articles

Reply to ‘Comment on “Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions” '

In this Reply, we address the issues raised by Gontchar and Chushnyakova in the preceding Comment [Gontchar and Chushnyakova, Phys. Rev. C 98, 029801 (2018)] with respect to the relation between the Eccles-Roy-Gray-Zaccone (ERGZ) analytical model of nuclear fission lifetime and previous models based on the mean-first passage time approach. We clarify that the originality of the ERGZ approach lies in the ability to provide closed-form expressions for the lifetime valid across the entire range of nuclear temperature.

Comment on “Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions”

We discuss several misleading statements made in the article by Eccles et al. [Phys. Rev. C 96, 054611 (2017)]. In particular, contrary to what is claimed in that paper, the analysis of the borders of Kramers formula applicability as a function of temperature using the mean first-passage time formula was performed earlier in the paper by Gontchar et al. [Phys. Rev. C 82, 064606 (2010)].

Erratum: Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions [Phys. Rev. C 96 , 054611 (2017)

Received 25 January 2018DOI:https://doi.org/10.1103/PhysRevC.98.019905©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFissionHydrodynamic modelsLow & intermediate energy heavy-ion reactionsStatistical phenomena & chaosThermal & statistical modelsNuclear Physics

Isospin Conservation in Neutron Rich Systems of Heavy Nuclei

It is generally believed that isospin would diminish in its importance as we go towards heavy mass region due to isospin mixing caused by the growing Coulomb forces. However, it was realized quite early that isospin could become an important and useful quantum number for all nuclei including heavy nuclei due to neutron richness of the systems [1]. Lane and Soper [2] also showed in a theoretical calculation that isospin indeed remains quite good in heavy mass neutron rich systems. In this paper, we present isospin based calculations [3, 4] for the fission fragment distributions obtained from heavy-ion fusion fission reactions. We discuss in detail the procedure adopted to assign the isospin values and the role of neutron multiplicity data in obtaining the total fission fragment distributions. We show that the observed fragment distributions can be reproduced rather reasonably well by the calculations based on the idea of conservation of isospin. This is a direct experimental evidence of the validity of isospin in heavy nuclei, which arises largely due to the neutron-rich nature of heavy nuclei and their fragments. This result may eventually become useful for the theories of nuclear fission and also in other practical applications.

Temperature dependence of nuclear fission time in heavy-ion fusion-fission reactions

Accounting for viscous damping within Fokker-Planck equations led to various improvements in the understanding and analysis of nuclear fission of heavy nuclei. Analytical expressions for the fission time are typically provided by Kramers' theory, which improves on the Bohr-Wheeler estimate by including the time-scale related to many-particle dissipative processes along the deformation coordinate. However, Kramers' formula breaks down for sufficiently high excitation energies where Kramers' assumption of a large barrier no longer holds. In the regime $T>1$ MeV, Kramers' theory should be replaced by a new theory based on the Ornstein-Uhlenbeck first-passage time method that is proposed here. The theory is applied to fission time data from fusion-fission experiments on $^{16}$O+$^{208}$Pb $\rightarrow$ $^{224}$Th. The proposed model provides an internally consistent one-parameter fitting of fission data with a constant nuclear friction as the fitting parameter, whereas Kramers' fitting requires a value of friction which falls out of the allowed range. The theory provides also an analytical formula that in future work can be easily implemented in numerical codes such as CASCADE or JOANNE4.

Dissipation strength of the tilting degree of freedom in fusion-fission reactions

The four-dimensional Langevin model was applied to calculate a wide set of experimental observables for compound nuclei, formed in heavy-ion fusion-fission reactions. A modified one-body mechanism for nuclear dissipation with a reduction coefficient ks of the contribution from a ”wall” formula was used for shapes parameters. Different possibilities of deformation-dependent dissipation coefficient for the K coordinate (γK) were investigated. Presented results demonstrate that the influence of the ks and γK parameters on the calculated quantities can be selectively probed. It was found that it is possible to describe experimental data with the deformation-dependent γK coefficient. One of the possibility is to use large values of γK � 0.2 (MeV zs) −1/2 for compact shapes featuring no neck and small values of γK � 0.0077 (MeV zs) −1/2 for elongated shapes. Fission still is one of the most interesting and challenging topics in nuclear physics providing a perfect opportunity to investigate the large scale evolution of initial compound nucleus into fission products. During the past two decades stochastic approach based on multidimensional Langevin equations has been extensively and rather successfully used to elucidate many problems of collective nuclear dynamics in fusion-fission reactions at high excitation energies [1, 2]. A reasonable choice of collective degrees of freedom for modeling shape evolution and considering particle evaporation allow modeling the complex interplay between static and dynamical effects in fission and succeeding in explaining a wide range of experimental data [3, 4].

Dynamics of neutron-induced fission ofU235using four-dimensional Langevin equations

Background: Langevin equations have been suggested as a key approach to the dynamical analysis of energy dissipation in excited nuclei, formed during heavy-ion fusion-fission reactions. Recently, a few researchers theoretically reported investigations of fission for light nuclei in a low excitation energy using the Langevin approach, without considering the contribution of pre- and post-scission particles and $\ensuremath{\gamma}$-ray emission.Purpose: We study the dynamical evolution of mass distribution of fission fragments, and neutron and $\ensuremath{\gamma}$-ray multiplicity for $^{236}\mathrm{U}$ as compound nuclei that are constructed after fusion of a neutron and $^{235}\mathrm{U}$.Method: Energy dissipation of the compound nucleus through fission is calculated using the Langevin dynamical approach combined with a Monte Carlo method. Also the shape of the fissioning nucleus is restricted to ``funny hills'' parametrization.Results: Fission fragment mass distribution, neutron and $\ensuremath{\gamma}$-ray multiplicity, and the average kinetic energy of emitted neutrons and $\ensuremath{\gamma}$ rays at a low excitation energy are calculated using a dynamical model, based on the four-dimensional Langevin equations.Conclusions: The theoretical results show reasonable agreement with experimental data and the proposed dynamical model can well explain the energy dissipation in low energy induced fission.

Effects of level density parameter on the superheavy production in cold fusion

By using semiclassical method and considering Woods–Saxon and Coulomb potentials, the level density parameter a was calculated for three superheavy nuclei 270110, 278112 and 290116. Obtained results showed that the value of level density parameter of these nuclei is near to the simple relation a ≈ A/10. In framework of the dinuclear system model, the effects of level density parameter on the probability of the formation of a compound nucleus, the ratio of neutron emission width and fission width, and evaporation residue cross-section of three cold fusion reactions 62 Ni +208 Pb , 70 Zn +208 Pb and 82 Se +208 Pb , leading to superheavy elements were investigated. The findings indicate that the level density parameter play a significant role in calculations of heavy-ion fusion–fission reactions. The obtained results in the case of a = A/12 have larger values in comparison with calculated level density parameter with Woods–Saxon potential (a WS ) and a = A/10. The theoretical results of the evaporation residue cross-section are very sensitive to the choice of level density parameter. The calculated values with a WS are in good agreement with experimental values.

Anisotropy of the angular distribution of fission fragments in heavy-ion fusion-fission reactions: The influence of the level-density parameter and the neck thickness

Using the Langevin dynamical approach, the neutron multiplicity and the anisotropy of angular distribution of fission fragments in heavy ion fusion-fission reactions were calculated. We applied one- and two-dimensional Langevin equations to study the decay of a hot excited compound nucleus. The influence of the level-density parameter on neutron multiplicity and anisotropy of angular distribution of fission fragments was investigated. We used the level-density parameter based on the liquid drop model with two different values of the Bartel approach and Pomorska approach. Our calculations show that the anisotropy and neutron multiplicity are affected by level-density parameter and neck thickness. The calculations were performed on the ${}^{16}$O+${}^{208}$Pb and ${}^{20}$Ne+${}^{209}$Bi reactions. Obtained results in the case of the two-dimensional Langevin with a level-density parameter based on Bartel and co-workers approach are in better agreement with experimental data.

Study of fusion cross-section in heavy-ion fusion-fission reactions at around fusion barrier energies using the Langevin dynamical approach

Coupled Langevin equations and Monte Carlo simulation were used to calculate the fusion cross-section in heavy-ion fusion-fission reactions. The effect of dynamical parameters on the distance of centers of two colliding nuclei is also investigated. Attention was focused on incident energies around the fusion barrier where measured values do not agree with results of different models. The calculations are done for typical systems. Finally, the results of the dynamical approach are compared with experimental data and the results obtained using the CCFULL code. The obtained results of the dynamical model are in satisfactory agreement with experimental data.

Statistical model of heavy-ion fusion-fission reactions

Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with the fission of fully equilibrated systems with fission lifetime estimates obtained via a Kramers-modified statistical model that takes into account the classical collective motion of the system about the ground state, the temperature dependence of the location and height of fission transition points, and the orientation degree of freedom. If the ``standard'' techniques for calculating fission lifetimes are used, then the calculated excitation-energy dependence of fission lifetimes is incorrect. We see no evidence to suggest that the nuclear viscosity has a temperature dependence. The strong increase in the nuclear viscosity above a temperature of $~1.3$ MeV deduced by others is an artifact generated by an inadequate fission model.

Fission Decay Widths for Heavy-Ion Fusion-Fission Reactions

Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with a Kramers-modified statistical model which takes into account the collective motion of the system about the ground state, the temperature dependence of the location of fission transition points, and the orientation degree of freedom. The strong increase in the nuclear viscosity above a temperature of approximately 1 MeV deduced by others is an artifact generated by an inadequate fission model.